Study On Variable Selection In Balanced Longitudinal Model

The different individuals or observation objects were observed repetitively at different times, then several observations of different individuals were obtained at different times, such data we call it as longitudinal data. Balanced longitudinal data are a kind of longitudinal data. The data were obtained by observing the different observation objects at the same time, which can reflect the change of different individuals over time. Balanced longitudinal data have been widely used in medical and social sciences research. When analyzing such data, the variables selection is the primary problem to be solved. Lasso and its related methods have a good effect in the variable selection.In this paper, the adaptive Lasso method and its subsequent improved adaptive elastic net method are used to processing the variables selection problem of the balanced longitudinal data model The regression coefficients that affect the smaller independent variables compress to zero, by adding constraints to the objective function. The main work is as follows.In the first chapter, we have discussed the practical application value of the balanced longitudinal data. We analyzed the research background and the significance of the variable selection of the balanced longitudinal data. In the second chapter, we have introduced the application and development of Lasso method and related methods in variable selection. In the first place, we have introduced the basic idea of Lasso method and related methods. Moreover, we have introduced the least angle regression algorithm, which effectively resolved the calculating of optimization problem with absolute value constraints as Lasso method and related methods. Finally, we also have introduced the Elastic net algorithm and group Lasso method with group effect, the SCAD method, the Adaptive Lasso method, the Adaptive Elastic net method. and so on with oracle property.In the third chapter and the fourth chapter, we have introduced the Adaptive Lasso method and the Adaptive Elastic net method into the variable selection of the balanced longitudinal data model respectively.We have proposed the Adaptive Lasso variable selection algorithm of the balanced longitudinal data and the Adaptive Elastic net algorithm of the balanced longitudinal data. We have analyzed the properties of above two methods, its oracle property and group effect. The two methods were validated by numerical experiments, and we have analyzed the numerical results.In the fifth chapter, we had analyzed the main factors that influencing the city's competitiveness. We have used the statistical data of twenty cities of twenty-eight indicators in 2011-2015 five years.Processing the primary data that we had and using the algorithm in the third chapter and the fourth chapter to analyzed, we have selected the greater impact on urban competition factors. The results have got a certain reference for a city to improve the city's competitiveness. Finally,this paper has summarized and proposed some proposals of the future research.